Geometry 21
Extra Practice 6.4
, 6.5, 6.6
Name ______________________________
Choose the term that most specifically classifies each figure. Choose from the following list of terms;
Parallelogram, Rectangle, Rhombus, Square, Trapezoid, Isosceles Trapezoid, Kite
1)
2)
3)
_____________________
______________________
____________________
4)
5)
6)
_______________________
_______________________
______________________
Complete each statement with always, sometimes, or never.
7. A rhombus is ______________ a parallelogram.
8. A parallelogram is ______________ a rhombus.
9. A rectangle is ______________ a rhombus.
10. A square is ______________ a rhombus.
11. A rhombus is ______________a square.
12. A rhombus is ______________ a hexagon.
Use the diagram at the right for the following exercises.
20. If ABCD is a rhombus, then AC  ________ .
21. If ABCD is a rhombus, then AC bisects  ________ and  ________ .
22. If ABCD is a rhombus, then 1  2   ________   ________ .
23. If ABCD is a rhombus, then BD bisects  ________ and  ________ .
24. If ABCD is a rhombus, then 3   ________   ________   ________ .
Find the values of the missing angles in each RHOMBUS below;
25.
26.
27.
28.
Algebra HIJK is a rectangle. Find the value of x and the length of each diagonal.
29. HJ = x and IK = 2x 7
30. HJ = 3x + 5 and IK = 5x 9
Find the measures of the numbered angles in each isosceles trapezoid.
31.
32.
33.
Algebra Find the value(s) of the variable(s) in each isosceles trapezoid.
34.
35.
36.
Find the lengths of the segments with variable expressions.
40.
41.
Classify the quadrilateral, then find the values of the variables.
ANSWERS:
1) Rhombus
7) always
2) kite
8) sometimes
3) square
9) sometimes
4) isos. Trapezoid
10) always
11) sometimes
20) BD
Parallelogram
kite
Rhombus
12) never
23) <ADC and <ABC
24) <4 , <8, <7
square
25) 59, 90, 90, 59
26) 38, 90, 90, 38
27) 51, 51, 39, 39
6) parallelogram
21) <BCD and <BAD
22) <5 and <6
isos. Trap
5) rectangle
28) 41, 90, 41, 49
29) x = 7, 7, 7
34) x = 4
30) x=7, 26, 26
35) x = 16, y = 116
32) 101, 79
33) 67, 113
36) x = 1
40) x = 10, LM=16, TU=24, QP=32
4) rhombus, x=2, y=10
31) 96, 84
41) x=3, BC=27, TU=19.5, KH=12
5) rectangle, x = 4, y = 8
6) isos. Trap., x = 3
7) kite, x = 7, y = 30
Lessons 6-4 and 6-5
For each parallelogram, determine the most precise name and find the measures of the numbered
angles.
1.
4.
2.
3.
5.
7. Use the information in the figure.
Explain how you know that ABCD
is a rectangle.
Explain.
6.
8. ABCD is a rhombus. What is
the relationship between 1 and 2?
M
16. If OT= 2a + b and ER = 80, and GY=3a-b, find a, b, & GY.
O
E
G
17.
T
R
Y
#1 - 12 Answer with Sometimes, Always or Never.
6.
AB  BC
7.
AC  BD
8.
 ABC   CDA
9.
 BAD &  ABC are complementary
10.
Find the best name for parallelogram ABCD using the given information:
a.
M is the midpoint of AC & DB
b.
AC  DB
___________________
(Use parallelogram ABCD for #6-9.)
___________________
___________________
___________________
___________________
___________________
2.
Given: ABCD is a kite with AB  BC,AD  CD
Prove:BD bisects AC
B
A
E
C
D
3.
Given: ABCD is a kite with AB  BC,AD  CD
Prove: BD bisects <ABC
B
A
E
C
D
5. Given: WXYZ is a parallelogram , 1  2
Prove: WXEZ is an isosceles trapezoid
Z
E
Y
1
W
2
X